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nyan_sandwich comments on Open Thread, July 1-15, 2013 - Less Wrong
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How does this square with chaos theory, which models behaviour that diverges greatly due to infinitesimal changes at the start?
What has it got to do with chaos theory?
Suppose you have two similar but extremely complicated systems that put compound pendulums to shame and both of which have different starting conditions. Would the state of one system ever be identical to the state of the other at any state that has occurred, or will occur, with system two?
No, with extremely high probability.
How does that relate to whatever Thomas was saying? For that matter, what is Thomas saying?
Are you sure?
That's a really cool proof, but phase space can be exponentially large, especially for an "extremely complicated" system. It also requires finite bounds on system parameters.
For that to break my "extremely high probability", there would have to be relatively few orbits in the phase space approaching a space-filling set of curves, which is itself extremely unlikely, unless you can think up some pathological example.
It does weaken my statement, though.
He suggested that it was possible for a person to be repeated, mental state and all, given enough time. I thought to conceptualize the minds of people as being like extremely complicated systems with chaotic interactions to ask if his belief could be true.